Finite Group Databasebeta

← #28338473

Subgroups — #28338473

Order 13696.

226 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293377C211yesmaximal, characteristic, complemented
2#20292817C212yesmaximal
3#20292422C211yesmaximal, characteristic, complemented
4#20292418C212yesmaximal, complemented
5#455×C107C211yesmaximal, characteristic
6#16812107—21no—
7#16812102—22no—
8#16812101—21no—
9#16812090—22no—
10#16812090C2212yes—
11#16812086—22no—
12#16812024—22no—
13#16812024C2212yes—
14H(5,𝔽2)×C107C2211yescharacteristic
15#137×C107—21no—
16#124×C107C2211yescharacteristic
17#104×C107—21no—
18#100×C107C2211yescharacteristic
19C2×Dic214—21no—
20C22×Dic107D412yes—
21C4⋊Dic107—21no—
22C4⋊Dic107—21no—
23Dic107⋊C4—22no—
24Dic107⋊C4—22no—
25Dic107⋊C4—22no—
26Dic107⋊C4—42no—
27C22⋊Dic107—22no—
28C22⋊Dic107—22no—
29C22⋊Dic107—42no—
30C22⋊Dic107D412yes—
31C4×Dic107—21no—
32#41×C107—21no—
33#41×C107—41no—
34C2×Q8×C107D411yescharacteristic
35C2×D4×C107—22no—
36C2×D4×C107—41no—
37C2×D4×C107C2311yescharacteristic
38Q16×C107—41no—
39SD16×C107—41no—
40M16×C107—21no—
41C22⋊C4×C107—22no—
42C42×C107D411yescharacteristic
43C23×C107—22no—
44C23×C107C2×D412yes—
45Q8×C107—21no—
46Q8×C107—41no—
47D4×C107—21no—
48D4×C107—41no—
49D4×C107—42no—
50D4×C107—41no—
51C2×C4×C107—22no—
52C2×C4×C107—21no—
53C2×C4×C107—21no—
54C2×C4×C107—41no—
55C2×C4×C107C2×D411yescharacteristic
56C2×Dic107—22no—
57C2×Dic107—22no—
58C2×Dic107—42no—
59C2×Dic107—42no—
60Dic214—81no—
61C8×C107—41no—
62C22×C107—22no—
63C22×C107—42no—
64C22×C107—41no—
65C22×C107—82no—
66C22×C107#12011yescharacteristic
67C4×C107—21no—
68C4×C107—41no—
69C4×C107—41no—
70C4×C107—41no—
71Dic107—42no—
72Dic107—42no—
73Dic107—82no—
74C2×C107—21no—
75C2×C107—42no—
76C2×C107—81no—
77C2×C107B(4,𝔽2)11yescharacteristic
78#2201—1071nomaximal, Sylow
79C107#220111yescharacteristic, complemented, Sylow
80#563—1071no—
81#458—1072no—
82#455D10711yescharacteristic
83#354—1071no—
84#352—1072no—
85H(5,𝔽2)C2×D10711yescharacteristic
86#137—21no—
87C4⋊Q8—2141no—
88#126—2142no—
89#125—2141no—
90#124C2×D10711yescharacteristic
91#123—1072no—
92#123—2142no—
93C22⋊Q8—2142no—
94#104—21no—
95#100C2×D10711yescharacteristic
96#99—1072no—
97#99—2142no—
98#41—21no—
99#41—41no—
100C2×Q8—2141no—
101C2×Q8C22⋊D10711yescharacteristic
102C2×D4—22no—
103C2×D4—41no—
104C2×D4C22×D10711yescharacteristic
105C22×C4—1072no—
106Q16—41no—
107SD16—41no—
108M16—21no—
109C4⋊C4—4282no—
110C4⋊C4—2141no—
111C4⋊C4—2142no—
112C4⋊C4—2142no—
113C4⋊C4—2141no—
114C4⋊C4—2142no—
115C22⋊C4—22no—
116C22⋊C4—1072no—
117C22⋊C4—4282no—
118C22⋊C4—2142no—
119C22⋊C4—2142no—
120C42—2141no—
121C42C22⋊D10711yescharacteristic
122C23—22no—
123C23D4×D10712yes—
124Q8—21no—
125Q8—41no—
126Q8—8561no—
127D4—21no—
128D4—41no—
129D4—42no—
130D4—41no—
131C2×C4—22no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—41no—
135C2×C4—4282no—
136C2×C4—4282no—
137C2×C4—2142no—
138C2×C4—2142no—
139C2×C4C2×C22⋊D10711yescharacteristic
140C8—41no—
141C22—22no—
142C22—42no—
143C22—41no—
144C22—82no—
145C22#1681207711yescharacteristic
146C4—21no—
147C4—41no—
148C4—41no—
149C4—41no—
150C4—8562no—
151C4—4282no—
152C4—4282no—
153C2—21no—
154C2—42no—
155C2—81no—
156C2#2029281311yescharacteristic
subgroupG/H
centerC2#20292813
commutator, cosocleC2×D4×C107C23
FrattiniC2×D4C22×D107
Fitting#455×C107C2
socleC2×C107B(4,𝔽2)
prime radicalH(5,𝔽2)×C107C22
hypercenter#455D107
hypocenterC107#2201
LCSG ▷ C2×D4×C107 ▷ C22×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #455

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #20293377C2semidirect
3. #20292422C2semidirect
4. #20292418C2semidirect
79. C107#2201semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202933772
#202928172
#202924222
#202924182
#455×C1072
#2201107